Assortative mixing in networks

TL;DR

This paper introduces a measure for assortative mixing in networks, showing social networks are often assortative while technological and biological networks are disassortative, and analyzes their properties.

Contribution

It defines a new measure for assortative mixing and studies its implications through analytical and numerical models of networks.

Findings

Social networks are often assortatively mixed.

Technological and biological networks tend to be disassortative.

Assortative networks percolate more easily and are more robust to vertex removal.

Abstract

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. We define a measure of assortative mixing for networks and use it to show that social networks are often assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortative network, which we study both analytically and numerically. Within the framework of this model we find that assortative networks tend to percolate more easily than their disassortative counterparts and that they are also more robust to vertex removal.